Can a Progressive Web App work with devices on a local Network?

About your question to secure a web server, you will need to provide a certificate for it (if it is for dev purposes you can also generate it by yourself):

There are some solutions that provide already the boilerplate for you:

• Npm local web server (and they explain step by step how to secure the web server)

• Here the info to generate a self signed certificate and how to apply it

This should help you with the next steps (correct me if I misunderstood your requirements).